470 BEPOBT — 1882. 



the cross-head ensure that the forces with which c and c' press on any object 

 nipped between them shall be equal. 



Thus any eccentricity of wheel will not prevent both c and c' from acting 

 on it, and since they both press with equal force, no strain will be exerted on the 

 dead-centre support, L. 



If the axis of D is absolutely coincident with that of the screw, the angle 

 through which the screw is turned is simply (since, when the hand closes on the 

 wheel, it practically becomes part of it) the arc through which D is turned by 

 the motion of the crank ; but suppose the axes are not coincident, but are separated 

 by a distance f , having a component «' in the mean plane of the levers c c', 

 the circumferential motion of c is a{r + i'), and of c' a(r-e'), where a is the 

 angular motion given to D by the crank, and small. As both c and c' try to 

 impress their own motion on the rim of the wheel, slipping must occur at one or 

 the other, but at which, if both jaws are made alike, it would be impossible to say. 

 To avoid this uncertainty, c' is made a roller having its axis when closed on the 

 wheel parallel to that of the screw. It then becomes certain that if any slipping 

 occur from the want of coincidence in the axes of D and the screw, it will 

 take place only at c', and the angle through which the screw is turned at each 



revolution of the crank becomes a-r , where E is the length of N', 



K. — e 



The above description touches on most of the important points in the machine, 

 although there still remain many details and precautions against errors of various 

 kinds, which, though very necessary to the working of tlie instrument, it would be 

 tedious to describe at length. 



The leading objects which the author had in view in making the designs, and 

 which he believed to be very important in all work where a high degree of 

 accuracy is required, were — 



1. To supply the necessary and sufficient conditions only to determine the 

 motion of each part. 



2. To arrange that, where possible, errors of the first order in the workmanship 

 should only produce errors of the second order in the results. 



3. To allow the workman to concentrate his attention on the fulfilment of one 

 condition only to the highest degree of accuracy in each part, and that where one 

 or more other conditions have to be fulfilled by the same part, a lower order of 

 accuracy should be sufficient for them. For instance, in the guidance of the 

 platform which holds the gi-ating, the most important condition is that the straight 

 edge which guides it should be really straight, and tliis must be fulfilled with the 

 utmost accuracy which good workmanship can attain; it is also requisite that 

 the straight edge should be parallel to the axis of the screw, but this condition, 

 owing to the nature of the connection between the nut and the platform, need 

 only be satisfied approximately. 



The action of the di-iving machinery can best be indicated by the diagram, 

 fig. 4, of the operations which it performs durmg the ruling of one line. The 

 variety of operations there shown necessarily make the mechanism a little 

 complicated, and the author would only describe that part of it which com- 

 municates the reciprocating motion to the tool carriage. The conditions which 

 the reciprocating motion must fulfil are, (1) that the force applied to the tool 

 carriage must be constant in direction; (2) that the velocity should be constant 

 during the whole time that the tool is cutting ; (3) that there should be no shock 

 or jerk when the motion is reversed. 



From either end of the tool carriage, fig. 5, steel bands pass over the wheels 

 B c, and that which passes over c is brought back to awheel B' similar to B, and 

 on the same axis ; the axis is fixed, and B and B' revolve independently on it. 



Teeth are cut on the flanges of B and B' which gear with those on the larger 

 wheel, D. 



D is practically two wheels joined together, rather more than half the circum- 

 ference of each being bare of teeth. The toothed portions of D engage alternately 

 with B and B'. D, when in gear with B, winds the steel band on to B and ofl' B', 

 and vice versa, the tool carriage being drawn backwards and forwards in the process. 



